Basic Math Examples

$| \frac{- 5 n}{5} | = 2$

Step 1

Remove the absolute value term. This creates a $\pm$ on the right side of the equation because $| x | = \pm x$ .

$\frac{- 5 n}{5} = \pm 2$

Step 2

The complete solution is the result of both the positive and negative portions of the solution.

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Step 2.1

First, use the positive value of the $\pm$ to find the first solution.

$\frac{- 5 n}{5} = 2$

Step 2.2

Cancel the common factor of $- 5$ and $5$ .

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Step 2.2.1

Factor $5$ out of $- 5 n$ .

$\frac{5 (- n)}{5} = 2$

Step 2.2.2

Cancel the common factors.

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Step 2.2.2.1

Factor $5$ out of $5$ .

$\frac{5 (- n)}{5 (1)} = 2$

Step 2.2.2.2

Cancel the common factor.

$\frac{5 (- n)}{5 \cdot 1} = 2$

Step 2.2.2.3

Rewrite the expression.

$\frac{- n}{1} = 2$

Step 2.2.2.4

Divide $- n$ by $1$ .

$- n = 2$

Step 2.3

Divide each term in $- n = 2$ by $- 1$ and simplify.

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Step 2.3.1

Divide each term in $- n = 2$ by $- 1$ .

$\frac{- n}{- 1} = \frac{2}{- 1}$

Step 2.3.2

Simplify the left side.

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Step 2.3.2.1

Dividing two negative values results in a positive value.

$\frac{n}{1} = \frac{2}{- 1}$

Step 2.3.2.2

Divide $n$ by $1$ .

$n = \frac{2}{- 1}$

Step 2.3.3

Simplify the right side.

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Step 2.3.3.1

Divide $2$ by $- 1$ .

$n = - 2$

Step 2.4

Next, use the negative value of the $\pm$ to find the second solution.

$\frac{- 5 n}{5} = - 2$

Step 2.5

Cancel the common factor of $- 5$ and $5$ .

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Step 2.5.1

Factor $5$ out of $- 5 n$ .

$\frac{5 (- n)}{5} = - 2$

Step 2.5.2

Cancel the common factors.

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Step 2.5.2.1

Factor $5$ out of $5$ .

$\frac{5 (- n)}{5 (1)} = - 2$

Step 2.5.2.2

Cancel the common factor.

$\frac{5 (- n)}{5 \cdot 1} = - 2$

Step 2.5.2.3

Rewrite the expression.

$\frac{- n}{1} = - 2$

Step 2.5.2.4

Divide $- n$ by $1$ .

$- n = - 2$

Step 2.6

Divide each term in $- n = - 2$ by $- 1$ and simplify.

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Step 2.6.1

Divide each term in $- n = - 2$ by $- 1$ .

$\frac{- n}{- 1} = \frac{- 2}{- 1}$

Step 2.6.2

Simplify the left side.

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Step 2.6.2.1

Dividing two negative values results in a positive value.

$\frac{n}{1} = \frac{- 2}{- 1}$

Step 2.6.2.2

Divide $n$ by $1$ .

$n = \frac{- 2}{- 1}$

Step 2.6.3

Simplify the right side.

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Step 2.6.3.1

Divide $- 2$ by $- 1$ .

$n = 2$

Step 2.7

The complete solution is the result of both the positive and negative portions of the solution.

$n = - 2, 2$